**5. Translation of "Universal Symmetry Principle – Curie"3**

Pierre Curie (1859-1906, Figure 3) was crushed under the wheels of a horse drawn carriage on a Paris street, a great misfortune for the world science. One of the most splendid French scientists of all time died at the peak of his power. Curie's deep insights survive in just a few, unusually concise articles. For this reason, the impact of his ideas, especially those related to crystallography and the symmetry principle, were not fully realized for some time.

The life and scientific work of Curie is described in a modest book by his wife Marie Curie (1867-1934) (Curie, 1963). Her brief biography of her husband succeeded in fleshing-out some of Pierre's ideas on symmetry that were not found in his publications. Marie also conveyed a sense of her husband's simple character and his devotion to the abstract life of the mind. Marie wrote, "He could never accustom himself to a system of work which involved hasty publications, and was always happier in a domain in which but a few investigators were quietly working" (Curie, 1963).

Pierre Curie was born in Paris, the son and grandson of physicians. He was schooled at home, but began attending lectures at the Sorbonne at a comparatively early age. At 18 he obtained a licentiate in physics after which he worked as a laboratory assistant in charge of the practical operations of the *École municipale de physique et de chimie industrielles*. He served as an instructor in physics until his appointment as Professor at the Sorbonne in 1903.

Curie's first papers describing the discovery of piezoelectricity in tourmaline, quartz, and other crystals (1880-1882), were written with his brother Jacques. His doctoral dissertation (1895) was an investigation of magnetism and the distinctions among diamagnetic, paramagnetic, and ferromagnetic substances, especially their temperature dependences. Pierre was a collaborator in the studies of radioactivity initiated by his wife Marie Skłodowska Curie. This work led to their joint discovery of polonium and radium in 1898. In 1903 they were awarded the third Nobel Prize in physics, together with Henri Becquerel (1852-1908). However, less well known than Pierre's highly publicized and well recognized work on radioactivity, but arguably as important, were theoretical papers devoted to crystallography and symmetry.

<sup>3</sup> In his scientific work, Shafranovskii was driven to understand the well know fact that crystals frequently have lower morphological symmetry than that expressed by physical properties or by X-ray diffraction. He recognized that the dissymmetry of the medium was often responsible for "false" crystal morphologies. This relationship between dissymmetric cause and effect was understandable in terms of Pierre Curie's Universal Symmetry Principle. For this reason, the work of Curie was of special interest to Shafranovskii. And for this reason, we provide a translation of one of the last chapters of the second volume of the *History*: "University Symmetry Principle – Curie".

#### **Figure 3.** Pierre Curie.

14 Recent Advances in Crystallography

others.

time.

(Povarennyh, 1962), physics (Dorfman, 1974), and chemistry (Figurovsky, 1969) among

Pierre Curie (1859-1906, Figure 3) was crushed under the wheels of a horse drawn carriage on a Paris street, a great misfortune for the world science. One of the most splendid French scientists of all time died at the peak of his power. Curie's deep insights survive in just a few, unusually concise articles. For this reason, the impact of his ideas, especially those related to crystallography and the symmetry principle, were not fully realized for some

The life and scientific work of Curie is described in a modest book by his wife Marie Curie (1867-1934) (Curie, 1963). Her brief biography of her husband succeeded in fleshing-out some of Pierre's ideas on symmetry that were not found in his publications. Marie also conveyed a sense of her husband's simple character and his devotion to the abstract life of the mind. Marie wrote, "He could never accustom himself to a system of work which involved hasty publications, and was always happier in a domain in which but a few

Pierre Curie was born in Paris, the son and grandson of physicians. He was schooled at home, but began attending lectures at the Sorbonne at a comparatively early age. At 18 he obtained a licentiate in physics after which he worked as a laboratory assistant in charge of the practical operations of the *École municipale de physique et de chimie industrielles*. He served

Curie's first papers describing the discovery of piezoelectricity in tourmaline, quartz, and other crystals (1880-1882), were written with his brother Jacques. His doctoral dissertation (1895) was an investigation of magnetism and the distinctions among diamagnetic, paramagnetic, and ferromagnetic substances, especially their temperature dependences. Pierre was a collaborator in the studies of radioactivity initiated by his wife Marie Skłodowska Curie. This work led to their joint discovery of polonium and radium in 1898. In 1903 they were awarded the third Nobel Prize in physics, together with Henri Becquerel (1852-1908). However, less well known than Pierre's highly publicized and well recognized work on radioactivity, but arguably as important, were theoretical papers devoted to

3 In his scientific work, Shafranovskii was driven to understand the well know fact that crystals frequently have lower morphological symmetry than that expressed by physical properties or by X-ray diffraction. He recognized that the dissymmetry of the medium was often responsible for "false" crystal morphologies. This relationship between dissymmetric cause and effect was understandable in terms of Pierre Curie's Universal Symmetry Principle. For this reason, the work of Curie was of special interest to Shafranovskii. And for this reason, we provide a translation of one of the last chapters of the second

as an instructor in physics until his appointment as Professor at the Sorbonne in 1903.

**5. Translation of "Universal Symmetry Principle – Curie"3**

investigators were quietly working" (Curie, 1963).

crystallography and symmetry.

volume of the *History*: "University Symmetry Principle – Curie".

Physics and crystallography, explained Marie in the foreword to Pierre's collected works, were "two sciences equally close to him and mutually complementary in spirit. For him, the symmetry of phenomena were intuitive." (Curie, 1908). Thus, he was perfectly positioned to fully apply symmetry to physical laws. Still, distractions of work on radioactivity, adverse health effects associated with handling radium, and the burdens of fame left him wanting of more time to devote to his first loves, symmetry and crystallography. In her biography, Marie wrote, "Pierre always wanted to resume his works on the symmetry of crystalline media…After he was named professor at the Sorbonne. Pierre Curie had to prepare a new course…He was left great freedom in the choice of the matter he would present. Taking advantage of this freedom he returned to a subject that was dear to him, and devoted part of his lectures to the laws of symmetry, the study of fields of vectors and tensors, and to the application of these ideas to the physics of crystals."

The crystallographic legacy of Pierre Curie consists of only 14 extremely brief articles, each a classic. Curie's earliest contributions to crystallography are devoted piezoelectricity. Then follow the papers on the Universal Symmetry Principle. Finally, there is a small article on the relationship of crystal form to surface energy (Curie, 1885). This is now known as the Gibbs-Curie-Wulff rule.

It is commonly stated that piezoelectricity of crystals was discovered by the Curie brothers in 1880. This assertion must be qualified. In 1817, Häuy published a communication "On the electricity obtained in minerals by pressure" (Haüy, 1817). Pierre and Jacques Curie rediscovered this lost and incompletely described phenomenon. For sphalerites, boracites, calamine, tourmaline, quartz, Rochelle salt and other compounds, the Curie brothers showed that piezoelectricity can be present only in hemihedral crystals with inclined faces – in other words in acentric crystals – and that electric dipole moments can arise only along polar directions. Thus, knowing the crystal symmetry it became possible to predict the

#### 16 Recent Advances in Crystallography

orientation of electrical axes. "This was by no means a chance discovery. It was the result of much reflection on the symmetry of crystalline matter that enabled the brothers to foresee the possibilities of such polarization", wrote Marie (Curie, 1963).

**Figure 4.** Seven infinite point groups of symmetry: rotating cone, cone at rest, rotating cylinder, twisted cylinder, cylinder at rest, rotating or chiral sphere, and sphere at rest.

Quartz crystals were studied in the most detail. The brothers Curie carried out a series of careful experiments that enabled them to establish general principles of piezoelectricity and define the magnitude of the quartz piezoelectric coefficient. The most complicated part of experimental work concerned the measurement of electrostriction, the deformation of piezoelectric crystals by applying an electric field (Curie, 1889). They proved the existence of this phenomenon, known as the inverse piezoelectric effect, first theoretically predicted by Lippmann (1845-1921). Finally, they invented and developed a series of devices for the study of piezoelectricy including a press with a manometer, a tool combining a lever and microscope for the measurement of electrostriction, and an extremely accurate electrometer in which metallized quartz surfaces were used to collect charges generated when pressure was applied to the quartz (Mouline & Boudia, 2009). Curies' works on piezoelectricity were inspirational to giants such as Röntgen (1845-1923), Kundt (1839-1894), Voigt (1850-1919), and Ioffe (1880-1960), among others. Langevin (1872-1946) utilized the piezoelectricity of quartz to produce ultrasound that is now used for measuring sea depth and detecting underwater objects.

At this same time, Curie worked out his theory of symmetry in a pair of papers (Curie, 1884, 1885b). Unlike Hessel, Bravais, and Fedorov, Curie's approach to symmetry fully integrated physics with mathematics. His lattices were made from physical objects, not geometrical points. The vectoral and tensorial physical properties of which he was so well aware through experimental work on magnetism and piezoelectricity were poorly accounted for by point lattices. "Significant difficulties arise", he said, "when points have associated properties related to direction in space. Such points should be represented by geometric figures embodying both magnitude and direction"(Curie, 1885). In searching for the proper figures, Curie was the first to establish the seven so-called "infinite point groups of symmetry" (Figure 4) with an infinite order axes (*L*∞). Hessel identified only three: *L*∞∞*P* (∞*m*) (symmetry of the cone), *L*∞∞*L*2∞*PC* (∞/*mm*) (symmetry of the bi-cone or cylinder), and ∞*L*∞∞*PC* (∞/∞*m*) (symmetry of the sphere). Curie completed this set by adding four additional infinite groups: *L*∞ (∞) (symmetry of rotating cone), *L*∞∞*PC* (∞/*m*) (symmetry of rotating the cylinder), *L*∞∞*L*2 (∞2) (symmetry of the twisted cylinder), and ∞*L*∞ (∞/∞) (symmetry of the sphere lacking mirror planes; all diameters of such a sphere are twisted to the right or left).

16 Recent Advances in Crystallography

underwater objects.

orientation of electrical axes. "This was by no means a chance discovery. It was the result of much reflection on the symmetry of crystalline matter that enabled the brothers to foresee

**Figure 4.** Seven infinite point groups of symmetry: rotating cone, cone at rest, rotating cylinder, twisted

Quartz crystals were studied in the most detail. The brothers Curie carried out a series of careful experiments that enabled them to establish general principles of piezoelectricity and define the magnitude of the quartz piezoelectric coefficient. The most complicated part of experimental work concerned the measurement of electrostriction, the deformation of piezoelectric crystals by applying an electric field (Curie, 1889). They proved the existence of this phenomenon, known as the inverse piezoelectric effect, first theoretically predicted by Lippmann (1845-1921). Finally, they invented and developed a series of devices for the study of piezoelectricy including a press with a manometer, a tool combining a lever and microscope for the measurement of electrostriction, and an extremely accurate electrometer in which metallized quartz surfaces were used to collect charges generated when pressure was applied to the quartz (Mouline & Boudia, 2009). Curies' works on piezoelectricity were inspirational to giants such as Röntgen (1845-1923), Kundt (1839-1894), Voigt (1850-1919), and Ioffe (1880-1960), among others. Langevin (1872-1946) utilized the piezoelectricity of quartz to produce ultrasound that is now used for measuring sea depth and detecting

At this same time, Curie worked out his theory of symmetry in a pair of papers (Curie, 1884, 1885b). Unlike Hessel, Bravais, and Fedorov, Curie's approach to symmetry fully integrated physics with mathematics. His lattices were made from physical objects, not geometrical points. The vectoral and tensorial physical properties of which he was so well aware

the possibilities of such polarization", wrote Marie (Curie, 1963).

cylinder, cylinder at rest, rotating or chiral sphere, and sphere at rest.

An illustration of seven infinite point groups after Shubnikov is given in Figure 4 (enantiomorphs are not shown). Curie illustrated these groups by examples from physics. The chiral sphere was associated with an optically active liquid. The *L*∞∞*L*2 case corresponded to two identical cylinders placed one onto another, filled with a liquid, and rotating with the same speed in opposite directions around their common axis *L*∞. The symmetry of a cone (*L*∞∞*P*) was compared with the symmetry of electric field, and the symmetry of a rotating cylinder (*L*∞*PC*) with the symmetry of the magnetic field (Curie, 1894). Infinite point groups are important because all other point groups are subgroups thereof.

Curie was the first to distinguish electric and magnetic dipoles. (Curie, 1894) Therefore, for example, in cubic crystals *m*3*m* and 432 Curie considers the double number of axes compared to conventional notion: 6*L*4, 8*L*3, 12*L*2. Obviously, this approach was initiated by his studies of piezoelectricity in which it is essential to distinguish reversible and irreversible (polar) directions.

This profound approach to symmetry enabled Curie to discover a new symmetry element, the "periodically acting plane of symmetry." This symmetry element now corresponds to the improper rotation axis. Bravais, in his paper, *Note sur les polyèdres symétriques de la géométrie* (1849) "studied the symmetric polyhedra, but accounted only for proper rotation axes, centers of inversion, and mirror planes. He did not take into account periodically acting planes of symmetry," said Curie (1966). However, Curie did not know that this concept already had been proposed by Hessel in a different form, and by Gadolin in 1867 during his deduction of the 32 symmetry classes.

Almost simultaneously with Curie, Fedorov introduced mirror-rotation axes in his first book *Introduction to the Doctrine of Figures* (1855). Federov simultaneously discovered the mirror-rotation axes. In a letter to Schoenflies (1853-1926), Fedorov protested against calling the 32 crystal classes "Minnigerode groups". "In my opinion," he wrote, "this name is especially wrong, because in a paper by Curie as well as in my "Principles of doctrine on figures" (which, as I mentioned in my previous letter, was submitted for publication before Curie's paper) there were some new ideas, whereas the paper by Minnigerode (1837-1896)

#### 18 Recent Advances in Crystallography

did not contain anything new" (Bokii & Shafranovskii, 1951). This question of priority lost its meaning when Sohncke (1842-1897) discovered that Hessel was in fact the first.

In 1885, Curie published a small but very important paper *Sur la formation des cristaux et sur les constants capillaires de leurs differrentes faces* (Curie, 1885a) in which he established that a crystal or an assemblage of crystals in equilibrium with a solution adopts a form that minimizes the surface energy. This result was obtained by Gibbs (1839-1903) in 1878, however, his work languished in the literature, unappreciated for a long time. In his classic paper "On the problem of growth and dissolution rates of crystal faces", Wulff (1863-1925) expressed this idea in terms that were easily applied (Wulff, 1952). The Wulff theorem states that "The minimum of the surface energy for a crystalline polyhedron of fixed volume is achieved, when the faces are spaced from the same point on distances that are proportional to the surface free energies" (Wulff, 1952). This theorem results in the important consequence that the growth rates of crystal faces are proportional to the specific surface energies of the faces. Wulff gave only an approximate proof of this theorem.

The theorem of Gibbs-Curie-Wulff was intensively debated. In 1915, Ehrenfest (1880-1933) emphasized that vicinal faces of real crystals have higher surface energies. This fact formed the basis of the objections to Curie's idea by the Dutch inorganic chemist, Van Arkel (1893- 1976). But, this principle can be unconditionally applied only to the equilibrium shapes of the crystal.

In 1894, Curie published an especially important paper on symmetry: *Sur la symétrie dans les phénomènes physiques. Symétrie d'un champ électrique et d'un champ magnétique*. This paper begins with a following sentence: "I believe that it would be very interesting to introduce into the study of physical phenomena the property of symmetry, which is well known to crystallographers" (1894). This paper contains the most important ideas on the universal significance of symmetry. Reflections on these ideas can be found in the biographical sketch by Marie, *Pierre Curie, with the Autobiographical Notes of Marie Curie*: "It was in reflecting upon the relations between cause and effect that govern these phenomena that Pierre Curie was led to complete and extend the idea of symmetry, by considering it as a condition of space characteristic of the medium in which a given phenomenon occurs. To define this condition it is necessary to consider not only the constitution of the medium but also its condition of movement and the physical agents to which it is subordinated." And, "For this it is convenient to define the particular symmetry of each phenomenon and to introduce a classification which makes clear the principal groups of symmetry. Mass, electric charge, temperature, have the same symmetry, of a type called scalar, that of the sphere. A current of water and a rectilineal electric current have the symmetry of an arrow, of the type polar vector. The symmetry of an upright circular cylinder is of the type tensor" (Curie, 1963).

General statements found in the above paper are of great significance. "The characteristic symmetry of a given phenomenon is a maximal symmetry compatible with this phenomenon. The phenomenon can exist in the medium, which has a characteristic symmetry of this phenomenon or a symmetry of a subgroup of the characteristic symmetry. In the other words, some symmetry elements can coexist with some phenomena but they are not requisite. Some symmetry elements should be absent. That is, dissymmetry creates the phenomenon" (Curie, 1894).

18 Recent Advances in Crystallography

the crystal.

did not contain anything new" (Bokii & Shafranovskii, 1951). This question of priority lost

In 1885, Curie published a small but very important paper *Sur la formation des cristaux et sur les constants capillaires de leurs differrentes faces* (Curie, 1885a) in which he established that a crystal or an assemblage of crystals in equilibrium with a solution adopts a form that minimizes the surface energy. This result was obtained by Gibbs (1839-1903) in 1878, however, his work languished in the literature, unappreciated for a long time. In his classic paper "On the problem of growth and dissolution rates of crystal faces", Wulff (1863-1925) expressed this idea in terms that were easily applied (Wulff, 1952). The Wulff theorem states that "The minimum of the surface energy for a crystalline polyhedron of fixed volume is achieved, when the faces are spaced from the same point on distances that are proportional to the surface free energies" (Wulff, 1952). This theorem results in the important consequence that the growth rates of crystal faces are proportional to the specific surface

The theorem of Gibbs-Curie-Wulff was intensively debated. In 1915, Ehrenfest (1880-1933) emphasized that vicinal faces of real crystals have higher surface energies. This fact formed the basis of the objections to Curie's idea by the Dutch inorganic chemist, Van Arkel (1893- 1976). But, this principle can be unconditionally applied only to the equilibrium shapes of

In 1894, Curie published an especially important paper on symmetry: *Sur la symétrie dans les phénomènes physiques. Symétrie d'un champ électrique et d'un champ magnétique*. This paper begins with a following sentence: "I believe that it would be very interesting to introduce into the study of physical phenomena the property of symmetry, which is well known to crystallographers" (1894). This paper contains the most important ideas on the universal significance of symmetry. Reflections on these ideas can be found in the biographical sketch by Marie, *Pierre Curie, with the Autobiographical Notes of Marie Curie*: "It was in reflecting upon the relations between cause and effect that govern these phenomena that Pierre Curie was led to complete and extend the idea of symmetry, by considering it as a condition of space characteristic of the medium in which a given phenomenon occurs. To define this condition it is necessary to consider not only the constitution of the medium but also its condition of movement and the physical agents to which it is subordinated." And, "For this it is convenient to define the particular symmetry of each phenomenon and to introduce a classification which makes clear the principal groups of symmetry. Mass, electric charge, temperature, have the same symmetry, of a type called scalar, that of the sphere. A current of water and a rectilineal electric current have the symmetry of an arrow, of the type polar vector. The symmetry of an upright circular cylinder is of the type tensor" (Curie, 1963).

General statements found in the above paper are of great significance. "The characteristic symmetry of a given phenomenon is a maximal symmetry compatible with this phenomenon. The phenomenon can exist in the medium, which has a characteristic symmetry of this phenomenon or a symmetry of a subgroup of the characteristic symmetry. In the other words, some symmetry elements can coexist with some phenomena but they are

its meaning when Sohncke (1842-1897) discovered that Hessel was in fact the first.

energies of the faces. Wulff gave only an approximate proof of this theorem.

Curie gave much broader interpretations to the concept "dissymmetry" than did Pasteur. He ascribed dissymmetry to the absence of symmetry elements that actuate some physical properties. For example, in the tourmaline crystal (*L*33*P* – 3*m*) the absence of the perpendicular symmetry plane gives the polar character to the *L*3 axis. This polarity makes pyroelectricity in tourmaline possible. For Curie, dissymmetry, the absence of symmetry, was as palpable as symmetry itself. He believed that the dissymmetric elements (e.g. a dissymmetry plane is any plane that is *not* a symmetry plane, a dissymmetry axis is any axis that is *not* a symmetry axis) could give a deeper insight into the physical meaning of phenomena. However, the infinite number of dissymmetry elements, unlike the very restricted number of symmetry elements, forces us to operate with the latter.

Shubnikov best characterized Curie's emphasis on dissymmetry: "symmetry must not be considered without its antipode – dissymmetry. Symmetry treats those phenomena at equilibrium, dissymmetry characterizes motion. The common conception of symmetrydissymmetry is inexhaustible" (Shubnikov, 1946).

Curie formulated several important consequences to what is now called Curie's Universal Principle of Symmetry-Dissymmetry. "Superimposition of several phenomena in one and the same system results in addition of their dissymmetries. The remaining symmetry elements are only those that are characteristic of both phenomena considered separately. If some causes produce some effects, the symmetry elements of these causes should be present in the effects. If some effects reveal dissymmetry, this dissymmetry should be found in the causes" (Curie, 1894).

The statements cited above were illustrated by Curie with the infinite symmetry classes. He emphasized the special importance of class *L*∞∞*P:* "Such a symmetry is associated with the axis of the circular cone. This is the symmetry of force, velocity, and the gravitational field, as well the symmetry of electric field. With respect to symmetry, all these phenomena may be depicted with an arrow" (Curie, 1894).

In fact, consequences of the association of symmetry *L*∞∞*P* with gravity are inexhaustible. For example, it explains evolution of the symmetry in organic life. The simplest organisms evolved in a medium of spherical symmetry (∞*L*∞∞*PC* (∞/∞*m*)) such as the protozoan suspended in a homogeneous fluid. Then the cone symmetry (*L*∞∞*P* (∞*m*)), that describes gravity begins to exert its influence pinning life to the ground. The plane symmetry *P*(*m*) is actualized for moving organisms. Thus, the evolution of the organic life is controlled by the following sequence of desymmetrization of the medium: ∞/∞*m* > ∞*m* > *m* (Shafranovskii, 1968; Spaskii & Kravtsov, 1971).

Likewise, in mineralogy (Shafranovskii, 1974) detailed investigations of real, naturally occurring crystals requires a thorough knowledge on the medium in which the crystals were formed. Curie's principle does not allow us to consider the resulting crystal in the absence of its growth medium because the symmetry of the growth medium is superimposed on the

#### 20 Recent Advances in Crystallography

symmetry of the growing crystal. The resulting form of the crystal can preserve only those symmetry elements that coincide with the symmetry elements of the growth medium. Of course, the internal symmetry, the crystal structure, does not change. The observed crystal morphology is a compromise resulting from the superimposition of two symmetries: internal symmetry of the crystal and the external symmetry of the medium. Thus, distorted crystal shapes, frequent in nature, are indicators of growth medium dissymmetry.

Curie's thoughts on symmetry have been only recently duly appreciated. Vernadsky was an advocate in his declining years. He wrote posthumously, "More than 40 year ago, in unfinished works interrupted first by the distraction of radium and then by death, Pierre Curie for the first time showed that the symmetry principle underlies all physical phenomena. Symmetry is as basic to physical phenomena as is the dimensionality of geometrical space because symmetry defines the physical state of the space – *état de l'éspace*. I have to stop here and emphasize the often forgotten importance of the force of personality. The premature depth of Curie at the peak of his powers stopped progress in this field for decades. Curie understood the significance of symmetry in physical phenomena before the causal relationship between symmetry and physical phenomena was not realized. He found the significance of this relationship previously overlooked" (Vernadsky, 1975).

Vernadsky writes: "The physically faithful definition [of symmetry], that we encounter throughout this book, was given by Curie…This is representation of a symmetry as a state of the earth, i.e. geological, natural space, or, more accurately as states of the space of natural bodies and phenomena of our planet Earth. Considering the symmetry as a state of the earth space it is necessary to emphasize the fact was expressed by Curie and recently stressed by A.V. Shubnikov, that the symmetry manifests itself not only in a structure but also in motions of natural bodies and phenomena" (Vernadsky, 1957).

Vernadsky knew Curie, whom he describes as "charming but lonely" (Vernadsky, 1965).

Detailed and very clear analyses of crystallographic ideas by Curie is presented in Shubnikov's paper "On the works of Pierre Curie in the field of symmetry" (Shubnikov, 1988): "P. Curie is known to broad audience of scientists as an author of influential works in the field of radioactivity. But he is almost unknown as the author of profound studies in the field of symmetry and its applications to physics. However, these studies, if they were continued by P. Curie, could have hardly less significance for development of natural science than his works on radioactivity for development of chemistry and physics."

Shubnikov noted that Curie's papers were "extremely concise", a style that did not lend itself to the general the acceptance of ideas that were before their time. He forecast that future generations would need to finalize Curie's ideas" (Shubnikov, 1988). At the same time, Shubnikov, with Koptsik argued that the Curie principle is part of a tradition, in that it is a generalization of the principles of his predecessors, Neumann and Minnegerode. This is true only in part. In fact, there is a vast difference between the scope of Curie's vision that expanded the significance of symmetry to all natural phenomena and the observations of Neumann and Minnegerode that were restricted to crystals. While, Curie is today rightly recognized as the forefather of the modern crystal physics, which is based entirely on symmetry laws, his ideas on symmetry in nature have penetrated into all branches of modern science.
